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Solving Using Quadratic Formula When D>0

A train trave...

Question

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

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Solution

Distance = 54 km
Let the average speed be x
Distance= 63km
The average speed to cover this distance = x+6
Total Time Taken= 3 hr.
D/S =t
therefore, 54/x + 63/x+6 = 3
54(x+6) +63x =3x(x+6)
$3 x^{2} - 99 x - 324$ =0
x=36, -3
Hence x= 36km/hr

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